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hi there welcome to my videos on Elementary differential equation this is video number eight for chapter nine the topic is partial differential equations in the previous video we derived the formal solution for wave equation lets summarize it here so here is the wave equation and we have boundary conditions which are dirichlet boundary condition and homogeneous and then we have initial conditions given in the form of an U axis zero and U sub T at X and zero of being the function of X and GX so the formal solution expressed in terms of the series is this so you sum up all the solutions u n which are called the eigenfunctions and they are like this they are cosine and sine combinations in t times a sine function in x so here the um frequency of oscillation W depends on the length L and that depends on the index n and then Lambda is in just the c times Omega n and then here the coefficients c n and the N depend on the initial condition c n depends on F and DN depend on G and C N can be
